Question

lesson practice 7.1.07
problems 1 - 4: here is part of a scale drawing of zahras office. the scale is 6 centimeters to 15 feet.

1. what are the dimensions of the actual office?
2. what is the actual area of her office?
3. zahra wants to put a couch in her office that is 3 feet wide. how wide would the couch be if it were drawn on the scale drawing?
4. fabianas office is near zahras office and measures 4 centimeters by 8 centimeters in the scale drawing. is fabianas office twice the area of zahras office? explain

Explanation:

Step1: Find the conversion factor

The scale is 6 cm to 15 feet. So the conversion factor is $\frac{15}{6}=\frac{5}{2}$ feet per cm.

Step2: Find actual dimensions of Zahra's office

The scale - drawing dimensions of Zahra's office are 2 cm by 4 cm.
The actual length $l$: $l = 4\times\frac{5}{2}=10$ feet.
The actual width $w$: $w = 2\times\frac{5}{2}=5$ feet.

Step3: Calculate the actual area of Zahra's office

The area formula is $A=l\times w$. So $A = 10\times5=50$ square - feet.

Step4: Find the scale - drawing width of the couch

Let $x$ be the width of the couch on the scale drawing. We know that $\frac{6}{15}=\frac{x}{3}$. Cross - multiply: $15x=6\times3$, so $x=\frac{6\times3}{15}=1.2$ cm.

Step5: Find actual dimensions and area of Fabiana's office

The scale - drawing dimensions of Fabiana's office are 4 cm by 8 cm.
The actual length $L$: $L = 8\times\frac{5}{2}=20$ feet.
The actual width $W$: $W = 4\times\frac{5}{2}=10$ feet.
The actual area $A_F$: $A_F = 20\times10 = 200$ square feet.
Since the area of Zahra's office is 50 square feet, and $\frac{200}{50}=4$, Fabiana's office is 4 times the area of Zahra's office, not 2 times.

Answer:

1. The actual dimensions of Zahra's office are 5 feet by 10 feet.
2. The actual area of Zahra's office is 50 square feet.
3. The width of the 3 - foot wide couch on the scale drawing is 1.2 cm.
4. Fabiana's office is not twice the area of Zahra's office. Fabiana's office is 4 times the area of Zahra's office because the actual area of Fabiana's office is 200 square feet and the actual area of Zahra's office is 50 square feet.